Abstract
Firstly, this paper gives the Cauchy-type integral formula and the Plemelj formula of hypermonogenic functions on unbounded domains and discusses the Hölder continuity of the quasi-Cauchy-type singular integral operator for hypermonogenic functions on unbounded domains. Secondly, this paper studies the relation between and and introduces the modified quasi-Cauchy-type singular integral operator . Finally, this paper proves the existence and uniqueness of the fixed point of the operator by the Banach’s Contraction Mapping Principle and gives a Mann iterative sequence which strongly converges to the fixed point of the operator .
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